Although the graph is attributed by the Channel 4 programme to “Svensmark and Christensen” it was first published in a paper by Friis-Christensen and Lassen, Science 254, 698 (1991), see
http://tinyurl.com/39dyse.

The number of sunspots change in a cyclical way over a time period of about 11 years, but this “solar cycle length” varies from cycle to cycle. The documentary reports that Friis-Christensen and Lassen found a good
correlation between solar cycle length and temperature. However, the documentary does not mention
that after corrections and updates to their original paper the correlation after 1975 disappeared
(see for instance Kristjánsson, 2001,
http://tinyurl.com/yvc8zu, PDF); with the temperature rapidly increasing while the solar curve remains flat. The solar
(red) line in the documentary ends in 1975 before this break-down in the correlation began,
presenting a deeply misleading picture.

These later corrections in the scientific literature are summarized by Damon and Laut in a paper in
EOS, Transactions American Geophysical Union, 2004 (abstract at
http://tinyurl.com/2m5jwk, full version at:
http://tinyurl.com/q7wg5, PDF). Damon and Laut summarise the findings of a number of peer reviewed papers, which show:

… that the apparent strong correlations displayed on these graphs have been
obtained by incorrect handling of the physical data. The graphs are still widely referred to in the
literature, and their misleading character has not yet been generally recognized.